A Madison Square Treat, From Rome Featured

New York has enjoyed a spectacular shift in the quality, quantity and variety of its street food in the past five years. Rome, however, has more or less remained wedded to fried rice balls and square pizza slices despite its millennial history of fast and cheap street food.

And yet, when the biannual Mad. Sq. Eats festival opens on Friday, it is a Roman snack that may threaten to upstage its New York counterparts.

For the duration of the monthlong festival, Stefano Callegari, a pizzaiolo from Rome, will take thick, spongy triangles of pizza bianca (a flatbread), slice them open on one side and stuff them with traditionally Roman fillings like trippa alla romana (stewed tripe), coda alla vaccinara (braised oxtail), seppie con piselli (cuttlefish with peas) and lingua con salsa verde (tongue with a garlicky parsley sauce). The three-sided bread pocket, which he calls a trapizzino, is served in a folded paper holder to catch any leaks.

The name trapizzino is a play on words, combining tramezzino (a triangular sandwich served in cafes) and pizza. Unlike the calzone or calzoncino, the bread for a trapizzino is baked separately, toasted to order, then stuffed with the requested filling. It had its debut at Mr. Callegari’s pizza-by-the-slice shop 00100 in Rome’s Testaccio district in 2008, quickly gaining popularity.

While the fillings are deeply rooted in the Roman classics, the concept takes cues from other Italian cities where street food culture is strong. “Florence has its many tripe stalls, and Palermo is famous for spleen sandwiches,” Mr. Callegari said. “I think this way of eating tripe and oxtail in Rome can eventually become a local custom like those.”

The Mad. Sq. Eats festival will be the snack’s first appearance abroad. It will be sold at the stall run by the Brooklyn restaurant Broken English, which will only be selling the trapizzino and beverages. The restaurant, which is currently closed, is in the process of rebranding, and will reopen next month as Broken English Osteria, with a new Roman-oriented menu.

The decision to involve Mr. Callegari came after Fabio Ciafaloni, an owner of Broken English, tried a trapizzino in Rome. “It is a simple and appealing dish, and there isn’t anything like it in New York,” Mr. Ciafaloni said. “We thought it would be the ideal product to help us relaunch the restaurant with this strong Roman theme. The fillings will be authentic and the ingredients will be local.”

There is one change Mr. Callegari has made to his distinctly Roman snack for the benefit of the New York audience: the inclusion of vegetarian options like a Sicily-inspired caponata and Tuscan fagioli all’uccelletto (beans in tomato sauce).